Quantum Information Theory is a new field with potential implications for the conceptual foundations of Quantum Mechanics through density matrices. In particular, information entropies in Hilbert space representation are highly advantageous in contrast with the ones in real space representation since they can be easily calculated for large systems. Quantum information entropies have shown, through quantum mechanics concepts such as entanglement, several interesting critical points which are not present in the energy profile, such as depletion and accumulation of charge, non-nuclear attractors and bond breaking/formation regions. In this work, von Neumann informational entropies are employed to characterize dendrimers. These nanostructured molecules are highly branched, star-shaped macromolecules which are defined by three components: a central core, an interior dendritic structure (the branches), and an exterior surface with functional surface groups. Monodisperse dendrimers are synthesized by step-wise chemical methods to give distinct generations (G0, G1, G2, ...) of molecules with narrow molecular weight distribution, uniform size and shape, and multiple (multivalent) surface groups. In particular, Polyamidoamine (PAMAM) dendrimers are the most common class of dendrimers suitable for many materials science and biotechnology applications which consist of alkyl-diamine core and tertiary amine branches.